## General Insurance

 Unit code: MATH69531 Credit Rating: 15 Unit level: Level 6 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

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#### Aims

The unit aims to provide students a grounding in modern stochastic modelling techniques of particular relevance to general non-life insurance.

#### Overview

This course gives an introduction into the mathematical techniques used in the field of non-life insurance (also referred to as general insurance). As the name implies, non-life insurance concerns all insurance products that are not dependent on the customer's survival or death. This concerns for instance the insurance of objects such as your bike and your car, travel insurance, accident insurance, fire insurance etc. For comparison, products such as pensions are life insurance rather than non-life insurance products.

We will mainly be involved with building and analysing stochastic models to make predictions about how many claims the insurance company should expect in the future for a certain portfolio of non-life insurance products, and how large these claims are. This is important to determine how much income the insurance company should generate, in the form of premium payments received from its customers, in order to be able to deal with the incoming claims, make a bit of profit as well and still not charge such high premiums nobody would be interested in buying the product.

The course MATH69542 Risk Theory in semester 2 further builds on the work done in this course.

#### Learning outcomes

Upon successful completion, the students are expected to be able to demonstrate a good understanding of the mathematical techniques introduced in this course and to apply these techniques to real-world (actuarial) problems.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

• Coursework 20%
• Examination at the end of the semester, two and a half hours duration, 80%.

#### Syllabus

• Elements of Statistics: point estimators, hypothesis testing and linear models.
• Two-person zero sum games, statistical games. Minimax criterion, Bayes criterion, (randomised) optimal decision rules in such games.
• Loss distributions in insurance, parametrized families of loss distributions and estimation of the parameters.
• Re-insurance strategies, excess of loss (stop-loss) re-insurance, proportional re-insurance.
• Risk models of short term general insurance (1): the individual risk model. Properties of the aggregate claim process. Stieltjes integrals and their application in individual risk models.
• Risk models of short term general insurance (2): the collective risk model. Modelling the claim number process, the aggregate claim process. Properties of the aggregate claim process. The compound Poisson model, the compound Binomial model, the compound Negative Binomial model.
• Risk models of short term general insurance (3): re-insurance in risk models. Excess of loss and proportional re-insurance. Parameter uncertainty (accident proneness).
• Risk models of short term general insurance (4): Panjer's recursive algorithm and similar algorithms.
• IBNR/Run-off triangles: chain ladder method.

#### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

#### Study hours

• Lectures - 33 hours
• Tutorials - 11 hours
• Independent study hours - 106 hours

#### Teaching staff

Kees Van Schaik - Unit coordinator